آنالیز ارتعاشی یک پانل کامپوزیت با استفاده از المان محدود اتفاقی: رویکرد ماتریس تصادفی

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

دانشکده مهندسی عمران، دانشگاه تبریز

10.22034/ceej.2025.65648.2414

چکیده

مدل‌سازی سیستم‌های دینامیکی عموماً نیازمند استفاده از روش‌های مدل‌سازی عددی با دقت بالا جهت کاهش خطاهای موجود در محاسبات می‌باشند. با این حال اگر یک سیستم دینامیکی نسبت به عدم‌قطعیت های موجود در مدل­سازی عددی و اندازه‌گیری‌های عملی حساسیت بالایی داشته باشد، جهت حصول پاسخ‌های دقیق این سیستم، به روش‌های مدل‌سازی جدیدتر و دقیق‌تری نیاز خواهد بود. یکی از چالش‌های اساسی ناشی از وجود عدم‌قطعیت در مسائل مهندسی در دسترس نبودن پارامتر صریحی برای توصیف رفتار سیستم جهت تحلیل دقیق می‌باشد. مشکلات ناشی از عدم‌قطعیت در مدل‌سازی، به‌خصوص در سازه‌هایی که در ساخت آن­ها از مواد کامپوزیتی استفاده شده است بیشتر نمود پیدا می‌کند. در تحقیق حاضر، شیوه مناسبی برای ارزیابی پارامترهای عدم‌قطعیت جهت دستیابی به پاسخ‌های دقیق سیستم دینامیکی، مورد مطالعه قرار گرفته است. بدین منظور یک مدل آزمایشگاهی از یک پانل کامپوزیتی تهیه گردید و همچنین رفتار دینامیکی آن به‌صورت عددی نیز مدل‌سازی شد. بدین منظور استفاده از مفهوم ماتریس‌های تصادفی جهت درنظر گرفتن پارامترهای عدم‌قطعیت در رفتار دینامیکی مدل، پیشنهاد و بررسی گردید و به‌منظور ارزیابی عملکرد روش پیشنهادی، نتایج حاصل از مدل عددی مربوطه با نتایج آزمایشگاهی مقایسه گردید. نتایج حاصل از این پژوهش نشان داد که روش ماتریس تصادفـی ویشـارت (Wishart random matrix) به‌طور قابل‌قبولی پارامترهای عدم‌قطعیت مورد نظر در پاسخ دینامیکی سیستم را ارزیابی و ردگیری می‌کند.

کلیدواژه‌ها

عنوان مقاله [English]

Vibration Analysis of a Composite Panel Using Stochastic Finite Element Method: A Random Matrix Approach

نویسندگان [English]

  • Ata Aghayi
  • Alireza Mojtahedi
  • Mohammad Ali Lotfollahi-Yaghin
  • Mohsen Kouhi
Department of Water Resources Engineering, University of Tabriz, Iran
چکیده [English]

Components and structures utilized in marine environments are subjected to high and persistent stresses resulting from wind, waves, and tides. Moreover, throughout their service life, these structures encounter harsh environmental conditions, particularly in splash zones. These conditions arise from the inherent variability and unpredictability of the marine environment, introducing a significant degree of uncertainty in assessments related to durability and performance. In recent decades, the use of composite materials in marine structures has gained significant attention, as they serve as suitable replacements for various components and systems, including ship hulls, propeller blades, propulsion system blades, as well as wind and tidal turbine blades, offering substantial benefits. Due to the presence of uncertainties, deterministic analyses cannot adequately reflect the performance of structures. However, if dynamic systems exhibit significant variability in parameters and mathematical descriptions due to parametric uncertainties and model uncertainties, reliance on this approach does not necessarily enhance confidence in simulation-based predictions. Unlike parametric uncertainty, model uncertainty presents substantial challenges because there are no explicit parameters available to describe its behavior in advance. In the present study, a set of mass-spring oscillators is randomly attached to a base system consisting of a simply supported monolithic plate, thereby introducing model uncertainty. While parametric uncertainty of the model can be addressed using the stochastic finite element method, the model uncertainty arises from the random attachment of mass-spring oscillators for each sample results in a different type of dynamic system. By examining the feasibility of employing a wavelet random matrix to represent a collection of dynamic systems that have emerged due to model perturbations, experiments conducted on a vibrational plate with randomly attached mass-spring oscillators demonstrate that the wavelet random matrix model can provide a satisfactory representation of model uncertainty in linear dynamic systems within the mid to high-frequency ranges.

کلیدواژه‌ها [English]

  • Uncertainty
  • Stochastic finite element method
  • Vibration analysis
  • Wishart random matrix
  • Composite panel

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نشریه مهندسی عمران و محیط زیست
دوره 55، شماره 120 - شماره پیاپی 120
پاییز 1404
آذر 1404
صفحه 33-43

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